(2/5)^{2x + 6} × (2/5)³ = (2/5)^{x + 2}. Find x.

Solution:

Given, the expression is (2/5)^{2x + 6} × (2/5)³ = (2/5)^{x + 2}.

We have to find the value of x.

Considering (2/5)^{2x + 6} × (2/5)³,

Using the law of exponents,

a^m × aⁿ = a^{m + n}

(2/5)^{2x + 6} × (2/5)³ = (2/5)^{2x + 6 + 3}

= (2/5)^{2x + 9}

Now, (2/5)^{2x + 9} = (2/5)^{x + 2}

On comparing the powers,

2x + 9 = x + 2

2x - x = 2 - 9

x = -7

Therefore, the value of x is -7.

✦ Try This: (2/3)^{x + 6} × (2/3)² = (2/2)^{x - 2}. Find x.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12

NCERT Exemplar Class 8 Maths Chapter 8 Problem 177(2)

(2/5)^{2x + 6} × (2/5)³ = (2/5)^{x + 2}. Find x.

Summary:

(2/5)^{2x + 6} × (2/5)³ = (2/5)^{x + 2}. The value of x is -7 using the law of exponents a^m × aⁿ = a^m+n

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